Related papers: A disk-covering problem with application in optica…
The input to the NP-hard Point Line Cover problem (PLC) consists of a set $P$ of $n$ points on the plane and a positive integer $k$, and the question is whether there exists a set of at most $k$ lines which pass through all points in $P$. A…
Given a set $P$ of $n$ points and a set $S$ of $m$ disks in the plane, the disk hitting set problem asks for a smallest subset of $P$ such that every disk of $S$ contains at least one point in the subset. The problem is NP-hard. In this…
Direct imaging of protoplanetary disks promises to provide key insight into the complex sequence of processes by which planets are formed. However imaging the innermost region of such disks (a zone critical to planet formation) is…
In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are…
Given a set of unit-disks in the plane with union area $A$, what fraction of $A$ can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved $1/4.41$. Motivated by the problem of channel-assignment…
In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and…
By a compact packing of the plane by discs, $P$, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc $C\in P$, there exists a sequence of discs $D_{0},\ldots,D_{m-1}\in P$ so that each…
Studies of debris disks around white dwarfs (WDs) have focused on infrared wavelengths because debris disks are much colder than the star and are believed to contribute to the spectrum only at longer wavelengths. Nevertheless, these disks…
The rarity of young massive stars combined with the fact that they are often deeply embedded has limited the understanding of their formation. Ground based mid-infrared (IR) interferometry is one way of securing the spatial resolution…
Optical imaging with microarcsecond resolution will reveal details across and outside stellar surfaces but requires kilometer-scale interferometers, challenging to realize either on the ground or in space. Intensity interferometry,…
We report on observations of circumstellar disks around young stars that have been obtained with the MIDI instrument, which is mounted on the VLT Interferometer and operates in the 10 micrometer atmospheric window. The maximum spatial…
We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…
We study the problem of covering a given point set in the plane by unit disks so that each point is covered exactly once. We prove that 17 points can always be exactly covered. On the other hand, we construct a set of 657 points where an…
Let $P$ be a set of points in the plane and let $m$ be an integer. The goal of Max Cover by Unit Disks problem is to place $m$ unit disks whose union covers the maximum number of points from~$P$. We are interested in the dynamic version of…
At present, the principal limitation on the resolution and contrast of astronomical imaging instruments comes from aberrations in the optical path, which may be imposed by the Earth's turbulent atmosphere or by variations in the alignment…
While doing optical study in an instrument similar to the interferometers dedicated to the Very Large Telescope (VLT), we have to take care of the pupil and focus conjugations. Modules with artificial sources are designed to simulate the…
Optics is an important subfield of physics required for instrument design and used in a variety of other disciplines, including materials science, physics, and life sciences such as developmental biology and cell biology. It is important to…
Turbulent coagulation in protoplanetary disks is known to operate on timescale far shorter than the lifetime of the disk. In the absence of mechanisms that replenish the small dust grain population, protoplanetary disks would rapidly lose…
In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove…
Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the…